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Partitions on a Set

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We denote the number of partitions of a set of n elements by P(n). Suppose the number of partitions of a set on n elements into k parts is denoted by P(n,k). Then obviously
P(n) = P(n,1) + P(n,2) + ..... + P(n,n)

Show that P(n,2) = 2^(n-1) - 1

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Set partitions are investigated. The solution is detailed and well-presented.

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